While that card will be in your budget, does not mean it will do what you want it to do.
If you expect it to play any modern games, or even older games unless they are quite a few years old, it won't.
For new, you won't really get anything faster, but that would also depend on your local market. Something like a GT 630 is about $30-40 used on ebay, only issue with buying off ebay is that you can't test the card first and you can get a bad card easily.
I'd look for a used card in your area like a Radeon 7750, GT630/730, Radeon R7 240, that should be in your budget used and will be much faster.